{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "AutoEncoderFibercopy.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/henkwymeersch/AutoencoderFiber/blob/master/AutoEncoderFiber.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "id": "GuDJI6Q5meSB",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Auto-encoder for a memoryless fiber-optic channel\n",
        "\n",
        "This script uses an auto-encoder (AE) for end-to-end learning of a non-linear memoryless fiber channel. The determines a good constellation and a good receiver. The achievable information rate is also computed. \n",
        "\n",
        "The system is of the form:\n",
        "$$\n",
        "x_{k+1}=x_k \\exp (j \\gamma L / K |x_k|^2) + n_k, k=0,..,K-1\n",
        "$$\n",
        "where $x_0$ is the input (a complex symbol), $\\gamma$ is the fiber nonlinearity parameter (typically around 1.2), $L$ is the fiber length, and $K$ is the number of amplification stages. The channel output is $x_K$. Finally, $n_k$ is white Gaussian noise. \n",
        "\n",
        "\n",
        "This code was is based on the paper\n",
        "\n",
        "Shen Li, Christian Häger, Nil Garcia, and Henk Wymeersch, \"Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learning,\" in *Proc. European Conference on Optical Communication* (2018) [arXiv:1804.07675](https://arxiv.org/pdf/1804.07675.pdf). \n",
        "\n",
        "The code was written by Christian Häger. Parts were provided by Shen Li. Integration and polishing by Henk Wymeersch. \n",
        "\n",
        "Remaining issues:\n",
        "*   returns NaN for too high input power\n",
        "\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "DTSyKzaDmeSN",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy.io as sio\n",
        "import math\n",
        "import time\n",
        "import sys\n",
        "import matplotlib.cm as cm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "IzWYJH3lmeSp",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def tf_print(tmp_var):\n",
        "    init = tf.global_variables_initializer()\n",
        "    sess = tf.Session()\n",
        "    sess.run(init)\n",
        "    print(sess.run(tmp_var))\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "sQzoQ8lumeS3",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "## START: these are the main parameters to set\n",
        "P_in_dBm=-2              # input power in dBm\n",
        "gamma = 1.27            # fiber nonlinearity (set to 0 zero for AWGN or 1.27 for a nonlinear channel)\n",
        "M = 16                   # constellation size\n",
        "\n",
        "# main network parameters and optimization parameters (to be modified for performance improvements)\n",
        "neurons_per_layer = 50 \n",
        "tx_layers = 2\n",
        "rx_layers = 3\n",
        "learning_rate = 0.001\n",
        "iterations = 50000\n",
        "stacks = 20\n",
        "minibatch_size = stacks*M\n",
        "## END: these are the main parameters to set\n",
        "\n",
        "\n",
        "# derived channel parameters\n",
        "channel_uses = 2 # this should be 2: the fiber code will break otherwise\n",
        "assert(channel_uses==2), \"channel uses should be 2\"\n",
        "L=2000             # fiber total length\n",
        "K=20               # number of amplification stages (more layers requires more time)\n",
        "sigma = 3.8505e-4*np.sqrt(2)  # N0= h*v*nsp*(G-1) sigma**2 = BW*N0 \n",
        "sigma2tot=K*sigma**2\n",
        "P_in=10**(P_in_dBm/10)*0.001\n",
        "Ess=np.sqrt(P_in)\n",
        "SNR=Ess**2/(sigma2tot)\n",
        "SNR_dB=10*np.log(SNR)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "8RbjEuy4LNYG",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#=====================================================#\n",
        "# Define the components of the computation graph\n",
        "#=====================================================#\n",
        "initializer = tf.contrib.layers.xavier_initializer()\n",
        "# transmitter\n",
        "W_tx = {}\n",
        "b_tx = {}\n",
        "for NN in range(tx_layers):\n",
        "    if NN == 0:\n",
        "        in_neurons = M\n",
        "    else:\n",
        "        in_neurons = neurons_per_layer\n",
        "    if NN == tx_layers - 1:\n",
        "        out_neurons = channel_uses\n",
        "    else:\n",
        "        out_neurons = neurons_per_layer\n",
        "    W_tx[NN] = tf.Variable(initializer([in_neurons, out_neurons]))\n",
        "    b_tx[NN] = tf.Variable(initializer([1, out_neurons]))\n",
        "        \n",
        "# receiver\n",
        "W_rx = {}\n",
        "b_rx = {}\n",
        "for NN in range(rx_layers):\n",
        "    if NN == 0:\n",
        "        in_neurons = channel_uses+1\n",
        "    else:\n",
        "        in_neurons = neurons_per_layer\n",
        "    if NN == rx_layers - 1:\n",
        "        out_neurons = M\n",
        "    else:\n",
        "        out_neurons = neurons_per_layer\n",
        "    W_rx[NN] = tf.Variable(initializer([in_neurons, out_neurons]))\n",
        "    b_rx[NN] = tf.Variable(initializer([1, out_neurons]))  \n",
        "\n",
        "# the encoder\n",
        "def encoder(x):\n",
        "    for NN in range(tx_layers-1):\n",
        "        x = tf.nn.tanh(tf.matmul(x, W_tx[NN]) + b_tx[NN])\n",
        "    x = tf.matmul(x, W_tx[tx_layers-1]) + b_tx[tx_layers-1]\n",
        "    return x\n",
        "\n",
        "# the decoder\n",
        "def decoder(x):\n",
        "    for NN in range(rx_layers-1):\n",
        "        x = tf.nn.tanh(tf.matmul(x, W_rx[NN]) + b_rx[NN])\n",
        "    x = tf.nn.softmax(tf.matmul(x, W_rx[rx_layers-1]) + b_rx[rx_layers-1])\n",
        "    return x\n",
        "\n",
        "# the non-dispersive fiber channel  \n",
        "def fiber_channel(x):\n",
        "    xr=x[:,0]\n",
        "    xi=x[:,1]\n",
        "    for segments in range(1,K+1):               \n",
        "        s=gamma*(xr**2+xi**2)*L/K        \n",
        "        xr=xr*tf.cos(s)-xi*tf.sin(s)\n",
        "        xi=xi*tf.cos(s)+xr*tf.sin(s)\n",
        "        xr=tf.add(xr,tf.random_normal(tf.shape(xr), mean=0.0, stddev=sigma))\n",
        "        xi=tf.add(xi,tf.random_normal(tf.shape(xi), mean=0.0, stddev=sigma)) \n",
        "    z=tf.stack([xr,xi,xr**2+xi**2]) \n",
        "    z=tf.transpose(z) \n",
        "    return z\n",
        "\n",
        "# average transmit power constraint\n",
        "def normalization(x): # E[|x|^2] = Es\n",
        "    return Ess*x / tf.sqrt(2*tf.reduce_mean(tf.square(x)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "_rlBVxfWmeTH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#=====================================================#\n",
        "# build the computation graph\n",
        "#=====================================================#\n",
        "X_tilde = tf.placeholder('float', [minibatch_size, M]) # one-hot vectors\n",
        "\n",
        "#grid coordinates for visulazing decision regions\n",
        "resolution=1000\n",
        "G = tf.placeholder('float', [resolution**2, channel_uses+1])\n",
        "\n",
        "X1=encoder(X_tilde)\n",
        "X = normalization(X1) # minibatch_size x channel_uses\n",
        "Y = fiber_channel(X)\n",
        "Z = decoder(Y)\n",
        "D = decoder(G)\n",
        "epsilon = 0.000001\n",
        "loss = -tf.reduce_mean(X_tilde*tf.log(Z+epsilon))\n",
        "MI=(np.log(M)-loss*M)/np.log(2)\n",
        "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
        "train = optimizer.minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "cYP38e2pmeTa",
        "colab_type": "code",
        "outputId": "fd6864b6-6478-4bba-8b1a-99fb70d925e8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 920
        }
      },
      "cell_type": "code",
      "source": [
        "#=====================================================#\n",
        "# parameter training\n",
        "#=====================================================#\n",
        "start_time = time.time()\n",
        "unitmatrix = np.eye(M)  \n",
        "training_set = np.tile(unitmatrix, [stacks, 1])\n",
        "init_op = tf.global_variables_initializer()\n",
        "sess = tf.Session()\n",
        "sess.run(init_op)\n",
        "MI_tmp=0\n",
        "totalloss=[]\n",
        "for i in range(1, iterations+1):\n",
        "    _, loss_tmp, MI_tmp = sess.run([train, loss, MI], feed_dict={X_tilde: training_set})\n",
        "    totalloss=np.append(totalloss, loss_tmp)\n",
        "    if i%1000==0 or i==1:\n",
        "        print('iteration ', i, ': loss = ', loss_tmp, '; Mutual information [bits] = ', MI_tmp)        \n",
        "elapsed = time.time() - start_time\n",
        "print(\"{0:.2f} seconds\".format(elapsed))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration  1 : loss =  0.17885368 ; Mutual information [bits] =  -0.12850097\n",
            "iteration  1000 : loss =  0.028006202 ; Mutual information [bits] =  3.3535295\n",
            "iteration  2000 : loss =  0.011281811 ; Mutual information [bits] =  3.7395804\n",
            "iteration  3000 : loss =  0.0055578933 ; Mutual information [bits] =  3.8717065\n",
            "iteration  4000 : loss =  0.005900917 ; Mutual information [bits] =  3.8637884\n",
            "iteration  5000 : loss =  0.004730115 ; Mutual information [bits] =  3.890814\n",
            "iteration  6000 : loss =  0.005254518 ; Mutual information [bits] =  3.878709\n",
            "iteration  7000 : loss =  0.0032975976 ; Mutual information [bits] =  3.923881\n",
            "iteration  8000 : loss =  0.0026089507 ; Mutual information [bits] =  3.9397771\n",
            "iteration  9000 : loss =  0.001929207 ; Mutual information [bits] =  3.9554677\n",
            "iteration  10000 : loss =  0.0034735291 ; Mutual information [bits] =  3.9198198\n",
            "iteration  11000 : loss =  0.0020205784 ; Mutual information [bits] =  3.9533587\n",
            "iteration  12000 : loss =  0.0019302426 ; Mutual information [bits] =  3.955444\n",
            "iteration  13000 : loss =  0.0027602636 ; Mutual information [bits] =  3.9362845\n",
            "iteration  14000 : loss =  0.001349867 ; Mutual information [bits] =  3.9688408\n",
            "iteration  15000 : loss =  0.0029932146 ; Mutual information [bits] =  3.9309072\n",
            "iteration  16000 : loss =  0.0007508879 ; Mutual information [bits] =  3.9826672\n",
            "iteration  17000 : loss =  0.0019698858 ; Mutual information [bits] =  3.9545288\n",
            "iteration  18000 : loss =  0.0018588252 ; Mutual information [bits] =  3.9570923\n",
            "iteration  19000 : loss =  0.0028716298 ; Mutual information [bits] =  3.9337137\n",
            "iteration  20000 : loss =  0.002332374 ; Mutual information [bits] =  3.9461615\n",
            "iteration  21000 : loss =  0.00052453595 ; Mutual information [bits] =  3.9878922\n",
            "iteration  22000 : loss =  0.0005966529 ; Mutual information [bits] =  3.9862273\n",
            "iteration  23000 : loss =  0.00065423944 ; Mutual information [bits] =  3.984898\n",
            "iteration  24000 : loss =  0.0022190292 ; Mutual information [bits] =  3.9487777\n",
            "iteration  25000 : loss =  0.0005131921 ; Mutual information [bits] =  3.9881537\n",
            "iteration  26000 : loss =  0.001012143 ; Mutual information [bits] =  3.9766364\n",
            "iteration  27000 : loss =  0.0011796795 ; Mutual information [bits] =  3.9727693\n",
            "iteration  28000 : loss =  0.0016018931 ; Mutual information [bits] =  3.9630234\n",
            "iteration  29000 : loss =  0.0016618859 ; Mutual information [bits] =  3.9616385\n",
            "iteration  30000 : loss =  0.00021583195 ; Mutual information [bits] =  3.995018\n",
            "iteration  31000 : loss =  0.0019067747 ; Mutual information [bits] =  3.9559858\n",
            "iteration  32000 : loss =  0.0012141239 ; Mutual information [bits] =  3.9719744\n",
            "iteration  33000 : loss =  0.0009799392 ; Mutual information [bits] =  3.9773798\n",
            "iteration  34000 : loss =  0.0015597316 ; Mutual information [bits] =  3.9639964\n",
            "iteration  35000 : loss =  0.0021589745 ; Mutual information [bits] =  3.9501643\n",
            "iteration  36000 : loss =  0.0018438756 ; Mutual information [bits] =  3.9574378\n",
            "iteration  37000 : loss =  0.0011696611 ; Mutual information [bits] =  3.9730003\n",
            "iteration  38000 : loss =  0.0013336143 ; Mutual information [bits] =  3.969216\n",
            "iteration  39000 : loss =  0.00085040426 ; Mutual information [bits] =  3.9803698\n",
            "iteration  40000 : loss =  0.0018855694 ; Mutual information [bits] =  3.9564753\n",
            "iteration  41000 : loss =  0.0006585914 ; Mutual information [bits] =  3.9847977\n",
            "iteration  42000 : loss =  0.0019125761 ; Mutual information [bits] =  3.9558516\n",
            "iteration  43000 : loss =  0.0027832282 ; Mutual information [bits] =  3.9357545\n",
            "iteration  44000 : loss =  0.000286943 ; Mutual information [bits] =  3.9933765\n",
            "iteration  45000 : loss =  0.0020027482 ; Mutual information [bits] =  3.9537704\n",
            "iteration  46000 : loss =  0.001009146 ; Mutual information [bits] =  3.9767056\n",
            "iteration  47000 : loss =  0.0018047865 ; Mutual information [bits] =  3.95834\n",
            "iteration  48000 : loss =  0.0005892061 ; Mutual information [bits] =  3.9863992\n",
            "iteration  49000 : loss =  0.002877311 ; Mutual information [bits] =  3.9335828\n",
            "iteration  50000 : loss =  0.0008200977 ; Mutual information [bits] =  3.9810696\n",
            "132.48 seconds\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "jasr9ooGmeTw",
        "colab_type": "code",
        "outputId": "6da1268b-b77f-4168-eef8-338c2a80d7cf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 660
        }
      },
      "cell_type": "code",
      "source": [
        "#=====================================================#\n",
        "# Visualization\n",
        "#=====================================================#\n",
        "#x,y grids\n",
        "x = np.arange(-0.1, 0.1, 0.0002)\n",
        "xx, yy = np.meshgrid(x, x)\n",
        "xg = xx.reshape(1000000,1)\n",
        "yg = yy.reshape(1000000,1)\n",
        "r = xg**2+yg**2\n",
        "xygrids = np.concatenate((xg, yg, r), axis=1)\n",
        "\n",
        "\n",
        "[constellation,receive_points,decision_regions] = sess.run([X,Y,D],feed_dict={X_tilde:training_set, G: xygrids})\n",
        "x = constellation[:, 0]\n",
        "y = constellation[:, 1]\n",
        "\n",
        "receive_x = receive_points[:, 0]\n",
        "receive_y = receive_points[:, 1]\n",
        "\n",
        "# plotting\n",
        "fig=plt.figure(figsize=(7, 7))\n",
        "ax = fig.add_subplot(2, 1, 1)\n",
        "plt.plot(totalloss)\n",
        "plt.xlabel('iteration')\n",
        "plt.ylabel('loss')\n",
        "\n",
        "fig = plt.figure(figsize=(7, 7))\n",
        "ax1 = fig.add_subplot(111)\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "ax1.scatter(x, y, c='b', marker='o')\n",
        "plt.axis('equal')\n",
        "xmax = max(abs(x))\n",
        "ymax = max(abs(y))\n",
        "max_axis = 1.2 * max(xmax, ymax)\n",
        "plt.xlim(-max_axis, max_axis)\n",
        "plt.ylim(-max_axis, max_axis)\n",
        "plt.show()\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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crCGWdnuu3/TRF5U0NHm4cqTdXLfrcweh1hCSEjs/1HzcfudRekeE0if65J6/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\nJUsYNWpUt+dHxVBERIKehkl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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8dc0237908>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
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Q//Vf/6XBwUE1NDQ4WTYAIMO5rHtduJum7DyXz7UCe9BXe9BXe9BXe6TqmiEz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8dbb7f19b0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "ATtx6VedmeUY",
        "colab_type": "code",
        "outputId": "72aa76c9-3f60-4307-cc85-8e1ac55cbedb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 428
        }
      },
      "cell_type": "code",
      "source": [
        "#=====================================================#\n",
        "# Decision regions\n",
        "#=====================================================#\n",
        "import matplotlib.cm as cm\n",
        "fig=plt.figure(figsize=(7, 7))\n",
        "plt.xlim(-max_axis, max_axis)\n",
        "plt.ylim(-max_axis, max_axis)\n",
        "z = np.argmax(decision_regions, axis=1).reshape(1000, 1000)\n",
        "plt.pcolormesh(xx, yy, z)\n",
        "cmap = cm.rainbow(np.linspace(0.0, 1.0, M))\n",
        "\n",
        "for k in range(minibatch_size):\n",
        "  index = k % M\n",
        "  plt.scatter(receive_x[k], receive_y[k], c=cmap[index], marker='.',s=50)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9bWai5IaWnt9XSfApqcr29bvwq9Nl8IVdWNMTwn+Ut+sebIA64ZaLgQYk3zvT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\nqUZupfq6kr21bOc6WmUupBbUmmCipmi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BhhllxEqNbMNsVRsDLTNWYKQ2VmpEGrB7oKk5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\n/xxXXHGFLteq5HrFli1bhrPPPhvXXntt1tdhq1AjIqLcZqv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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8dbe98f2b0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}